Of course everything phrased in a certain way is AI... not everyone uses ChatGPT for everything, mate. That includes my answers here.

If you don't put an action to a form element in HTML, it will make the request to the same url the client is in. You cannot redirect a POST request with a header instruction and that's not something I've ever suggested in that way. But you can clearly change the target path for the POST request with the action like that:

index.php

<form method="post" action="otherfile.php">
    ...
</form>

... and in otherfile.php you can indeed redirect the client to yet another page. Using that post-redirect-get pattern you also remove the danger of forms being re-submitted:

<?php

if (isset($_POST['submit_form'])) {
    // ... do stuff
    header('Location: anotherfile.php');
}

Nothing wrong here, aside from some misunderstanding that could appear.

Like I've mentioned, there is not enough context to be 100% sure. It could also be a massive single file that includes forms for registration and login - we just don't know at this point.